Stochastic rounding of numerical values

ABSTRACT

A method, computer readable medium, and system are disclosed for rounding numerical values. A set of bits from an input value is identified as a rounding value. A second set of bits representing a second value is extracted from the input value and added with the rounding value to produce a sum. The sum is truncated to produce the rounded output value. Thus, the present invention provides a stochastic rounding technique that rounds up an input value as a function of a second value and a rounding value, both of which were obtained from the input value. When the second value and rounding value are obtained from consistent bit locations of the input value, the resulting output value is deterministic. Stochastic rounding, which is deterministic, is advantageously applicable in deep learning applications.

FIELD OF THE INVENTION

The present invention relates to rounding numerical values, and more particularly, to circuits for performing stochastic rounding.

BACKGROUND

Reducing precision in representing numerical values for mathematical computations may be beneficial in certain circumstances. For example, 32-bit floating-point values can be replaced with less precise 16-bit floating-point values to reduce circuitry, power, and bandwidth for training of neural networks. The reduced precision values require only half the bandwidth during data transmission and less than half the die area and power consumption compared with using full precision values. However, the range of values that can be represented using a 16-bit floating-point format is much smaller than the range of values that can be represented using a 32-bit floating-point format. Numbers smaller than the smallest value represented by the 16-bit floating-point format are lost (i.e., turned to zero).

Stochastic rounding is a method that is conventionally used to extend numerical range. With traditional rounding, numbers are deterministically rounded up or down, for example values between 0.5 and 1 are rounded up to 1, values below 0.5 are always rounded down to 0. With stochastic rounding, the rounding is instead probabilistic. Specifically, 0.5% has 50% odds of being rounded up to 1 and 50% odds of being rounded down to 0, while 0.1 has 10% odds of being rounded up to 1 and 90% odds of being rounded down to 0.

With stochastic rounding, an individual rounding event can actually introduce more error, but on average over a long sequence of accumulations, the result will have less error. For example, when accumulating 1000 numbers with value 0.1 with traditional rounding after each number is accumulated, the result will be zero, whereas with stochastic rounding the result should be closer to the correct answer of 100.

Thus while stochastic rounding is preferable when applying an accumulate and round operation over a long series of numerical values, the challenge is implementing the random rounding behavior of stochastic rounding efficiently in software or hardware. One method could be to generate a random number for each rounding operation, but that is extremely expensive in terms of additional circuitry and/or power consumption. There is a need for addressing these issues and/or other issues associated with the prior art.

SUMMARY

A method, computer readable medium, and system are disclosed for rounding a numerical value. An input value represented by a first number of bits is received and a portion of the first number of bits of the input value is identified as a rounding value represented by a second number of bits. A second value is extracted from the input value and the rounding value is aligned with a rounding position within the second value, where the rounding position corresponds to a least significant bit of an output value represented by a third number of bits. The aligned rounding value and the second value are added to produce a sum and the sum is truncated to produce the output value.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a flowchart of a method for rounding numerical values, in accordance with an embodiment.

FIG. 2A illustrates a block diagram of a rounding unit, in accordance with an embodiment.

FIG. 2B illustrates rounding of a 23-bit mantissa to produce a 10-bit reduced bit width mantissa, in accordance with an embodiment.

FIG. 2C illustrates another block diagram of a rounding unit, in accordance with an embodiment.

FIG. 2D illustrates another flowchart of a method for rounding numerical values, in accordance with an embodiment.

FIG. 3 illustrates a parallel processing unit, in accordance with an embodiment.

FIG. 4A illustrates a general processing cluster within the parallel processing unit of FIG. 3, in accordance with an embodiment.

FIG. 4B illustrates a memory partition unit of the parallel processing unit of FIG. 3, in accordance with an embodiment.

FIG. 5A illustrates the streaming multi-processor of FIG. 4A, in accordance with an embodiment.

FIG. 5B is a conceptual diagram of a processing system implemented using the PPU of FIG. 3, in accordance with an embodiment.

FIG. 5C illustrates an exemplary system in which the various architecture and/or functionality of the various previous embodiments may be implemented.

DETAILED DESCRIPTION

A new rounding mechanism is described for reducing the bit width of a value from its original full bit width (N-bits) to a reduced bit width (M-bits). In an embodiment, a portion of the N bits of the value of a floating-point mantissa are used as a rounding value. A rounding position within the full bit width value is the position of the least significant bit of the reduced bit width value. In other words, bits to the right of the rounding position will be truncated to perform the bit width reduction. The number of fractional bits to the right of the rounding position to be truncated may be fixed, computed, or programmable. Similarly, the number of bits (M) in the reduced bit width value may be fixed, computed, or programmable. M determines the rounding position within the N-bit input value. All or less than N-bits of the original input value is used to produce a second value that is summed with the rounding value.

The rounding value is aligned to the right of the rounding position and added to the second value to compute a sum. In contrast, when conventional round-to-nearest is performed, a fixed value is summed with the full bit width value to compute a sum. In both cases, the fractional bits to the right of the rounding position within the sum are truncated to produce the reduced bit width value.

FIG. 1 illustrates a flowchart of a method 100 for rounding numerical values, in accordance with an embodiment. Although method 100 is described in the context of a processing unit, the method 100 may also be performed by a program, custom circuitry, or by a combination of custom circuitry and a program. For example, the method 100 may be executed by a GPU (graphics processing unit), CPU (central processing unit), or any processor capable of performing arithmetic computations. Furthermore, persons of ordinary skill in the art will understand that any system that performs method 100 is within the scope and spirit of embodiments of the present invention.

At step 110 an input value represented by a first number of bits is received. In an embodiment, the input value is represented in a floating-point format comprising an exponent and a mantissa. In another embodiment, the input value is represented in a fixed-point format.

At step 120, a portion of the first number of bits of the input value is identified as a rounding value represented by a second number of bits. In an embodiment, the portion of the first number of bits of the input value are identified within the mantissa. In an embodiment, the portion of the first number of bits of the input value that are identified are the least significant bits of the mantissa. In an embodiment, the portion of the first number of bits of the input value are identified within the fixed-point format value. In an embodiment, the portion of the first number of bits of the input value that are identified are the least significant bits of the fixed-point format value. In another embodiment, the portion of the first number of bits of the input value that are identified are a set of contiguous bits of the input value. In yet another embodiment, the portion of the first number of bits of the input value that are identified are a set of bits of the input value from predetermined bit locations of the input value.

At step 130, a second value is extracted from the input value. In an embodiment, the second value is the same value as the input value. In another embodiment, the second value is a less precise value of the input value. In yet another embodiment, the second value is represented by less bits than the input value. At step 140, the rounding value is aligned with a rounding position within the second value, where the rounding position corresponds to a least significant bit of an output value represented by a third number of bits. The rounding position is described in more detail in conjunction with FIG. 2B. At step 150, the aligned rounding value and the second value are added to produce a sum. At step 160, a fourth number of bits is truncated from the sum to produce the output value. In an embodiment, the fourth number of bits is determined such that the output value is the reduced bit width comprising the third number of bits. In an embodiment, the fourth number of bits is equal to the second number of bits. In an embodiment, the input value is a mantissa of a floating-point format number and the output value is an integer.

More illustrative information will now be set forth regarding various optional architectures and features with which the foregoing framework may be implemented, per the desires of the user. It should be strongly noted that the following information is set forth for illustrative purposes and should not be construed as limiting in any manner. Any of the following features may be optionally incorporated with or without the exclusion of other features described.

FIG. 2A illustrates a block diagram of a rounding unit 200, in accordance with an embodiment. The rounding unit 200 includes a threshold comparison unit 210, a multiplexer 215, and an accumulator 220. The rounding unit 200 receives a floating-point format value including an exponent and a mantissa of N bits. In an embodiment, the floating-point format value is represented using an IEEE (Institute of Electrical and Electronic Engineers) floating-point format. In an embodiment, the mantissa is rounded in accordance with the present invention.

The threshold comparison unit 210 compares the floating-point input with a threshold value. When the floating-point input is greater than or equal to the threshold value, a fraction value may be used as a rounding value to round the mantissa. The threshold value may be fixed, computed, or programmed. In an embodiment, the threshold value equals the smallest value that can be represented using a floating-point format with a reduced bit width. In another embodiment, the threshold value equals the largest value that can be represented using a floating-point format with a reduced bit width.

The threshold comparison unit 210 outputs a select signal to the multiplexer 215 that is used to select either the fraction value or a portion of the input value as the rounding value. In an embodiment, the portion of the mantissa is provided as an input to the multiplexer 215, where the mantissa is a first number of bits (N) and the portion of the mantissa includes less than N bits. The rounding unit 200 outputs a reduced mantissa having a third number of bits (M), where M is less than N.

The fraction value may be used to perform conventional IEEE 754-2008 rounding. The fraction value may be fixed, computed, or programmed. Otherwise, when the floating-point input is less than (i.e., not greater than or equal to) the threshold value, a portion of the mantissa is selected by the multiplexer 215 as a rounding value to round the mantissa. The threshold comparison unit 210 extracts a second value from the floating-point input. In an embodiment, the second value is a portion of the mantissa having fewer than N bits.

The accumulator 220 receives the second value and the rounding value and produces the reduced mantissa. The rounding value is aligned with a rounding position within the second value. The rounding position corresponds to a least significant bit of the reduced mantissa. The aligned rounding value is summed with the second value to produce a sum. The accumulator 220 truncates a number of bits from the sum to produce the reduced mantissa having a fewer number of bits than the mantissa of the input value.

In an embodiment, the input value includes a 23-bit mantissa of a floating-point format number and the output value generated by the rounding unit 200 is a 10-bit reduced mantissa. In another embodiment, the input value includes a 23-bit mantissa of a floating-point format number and the output value generated by the rounding unit 200 is a 7-bit mantissa. In yet another embodiment, the input value includes a 52-bit mantissa of a floating-point format number and the output value generated by the rounding unit 200 is a 23-bit mantissa.

FIG. 2B illustrates rounding of a 23-bit mantissa to produce a 10-bit reduced bit width mantissa, in accordance with an embodiment. In an embodiment, the 23-bit mantissa includes an implied leading one. In an embodiment, the 23-bit mantissa is reduced to a 10-bit reduced mantissa by summing the 8 lsbs (least significant bits) of the 23-bit mantissa aligned with the bits of the 23-bit mantissa that are to the right of the lsb of the 10-bit reduced mantissa. As shown in FIG. 2B, the 10 most-significant (MS) bits correspond to the reduced bit-width mantissa, where M=10. The 8 least significant (LS) bits (bits 16 through 23) of the 23-bit mantissa are used as an 8-bit rounding value that is aligned with the rounding position and summed with the 23-bit mantissa. A carry bit, generated by summing bits 11 through 18 with bits 16 through 23, increments the 10 MS bits when the carry bit is high. The resulting 23-bit sum is truncated to produce the 10-bit reduced mantissa.

In an embodiment, if the sum overflows during rounding, the sum is shifted to the right by one bit and then truncated. In an embodiment, the reduced mantissa is 7 bits. In other embodiments, the reduced mantissa is fewer or more bits. In some embodiment, the number of bits representing the input mantissa is greater than or less than 23 bits. In an embodiment, the rounding value or LS bits of the mantissa are optionally modified before the sum is computed. For example, the fraction value may be XOR'd with the LS bits of the mantissa, the fraction value may be used as a bit rotation count for the LS bits of the mantissa, or the fraction value may be used as a mask to select specific bits to the right of the rounding position within the mantissa to generate the rounding value.

FIG. 2C illustrates another block diagram of a rounding unit 250, in accordance with an embodiment. The rounding unit 250 includes a threshold comparison unit 212, a rounding value generation unit 225, and the accumulator 220. The rounding unit 250 receives a floating-point format value including an exponent and a mantissa of N bits.

One or more ranges and/or threshold values are defined corresponding to different rounding modes and the threshold comparison unit 212 receives a rounding mode that controls which of the threshold ranges or values are compared with the floating-point input. In an embodiment, when the floating-point input is greater than or equal to the threshold value, a fraction value may be used as a rounding value to round the mantissa. In another embodiment, when the floating-point input is within or outside a threshold range, the fraction value may be used as a rounding value to round the mantissa. The threshold value and/or the rounding mode may be fixed, computed, or programmed.

The threshold comparison unit 212 outputs a select signal to the rounding value generation unit 225 that is used to select either the fraction value or a portion of the input value as the rounding value. The rounding mode may be used to modify the rounding value. In an embodiment, the threshold comparison unit 212 extracts and provides a portion of the mantissa as an input to the rounding value generation unit 225, where the mantissa is represented by a first number of bits (N) and the portion of the mantissa includes less than N bits. In an embodiment, the rounding value extracted by the threshold comparison unit 212 is the LS bits of the mantissa. The rounding unit 250 outputs a reduced mantissa having a third number of bits (M), where M is less than N. In an embodiment, the rounding value selected by the rounding value generation unit 225 is the LS bits of the mantissa.

In an embodiment, the rounding value generation unit 225 modifies the rounding value or LS bits of the mantissa are optionally modified before the sum is computed. For example, based on the rounding mode, the fraction value may be XOR'd with the LS bits of the mantissa, the fraction value may be used as a bit rotation count for the LS bits of the mantissa, or the fraction value may be used as a mask to select specific bits to the right of the rounding position within the mantissa to generate the rounding value. The rounding mode and/or the fraction value may be fixed, computed, or programmed.

As previously described, the accumulator 220 receives the second value and the rounding value and produces the reduced mantissa. The rounding value is aligned with a rounding position within the second value. The rounding position corresponds to a least significant bit of the reduced mantissa. The aligned rounding value is summed with the second value to produce a sum. The accumulator 220 truncates a number of bits from the sum to produce the reduced mantissa having the third number of bits.

The rounding may be performed using a dedicated instruction, such as an instruction that converts a value having a first bit-width to a value having a second bit-width, where the second-bit width is less than the first bit-width. In an embodiment, one or more of the fraction value, the threshold range, the threshold value, and the rounding mode may be provided as an operand to the instruction. In an embodiment, the fraction value may be generated by an incrementor. The rounding operation may be selectively enabled for instructions that perform arithmetic operations (e.g., multiply accumulate, sum, etc.) and produce a reduced bit-width output. In an embodiment, the rounding value is returned along with the reduced bit-width value when the instruction(s) is executed.

FIG. 2D illustrates another flowchart of a method 260 for rounding numerical values, in accordance with an embodiment. Although method 260 is described in the context of a processing unit, the method 260 may also be performed by a program, custom circuitry, or by a combination of custom circuitry and a program. For example, the method 260 may be executed by a GPU (graphics processing unit), CPU (central processing unit), or any processor capable of performing arithmetic computations. Furthermore, persons of ordinary skill in the art will understand that any system that performs method 260 is within the scope and spirit of embodiments of the present invention.

At step 110 an input value represented by a first number of bits is received. In an embodiment, the input value is represented in a floating-point format comprising an exponent and a mantissa. At step 265, the threshold comparison unit 212 generates a select signal for the input value and either a threshold value or threshold range based on a rounding mode. In an embodiment, the threshold comparison unit 212 compares the input value with the threshold value and generates the select signal to select a fraction value when the input value is greater than the threshold value. In an embodiment, the threshold comparison unit 212 compares the input value with the threshold value and generates the select signal to select the fraction value when the input value is greater than or equal to the threshold value.

At step 270, the rounding value generation unit 225 determines if the select signal selects the fraction value, and if not, step 120 is completed to identify a portion of the input value to be selected as the rounding value before proceeding to step 275. In an embodiment, the portion of the input value is identified by connecting a subset of the wires for the mantissa to the rounding value generation unit 225. If, at step 270, the rounding value generation unit 225 determines that the select signal selects the fraction value, the rounding value generation unit 225 proceeds directly to step 275. At step 275, the rounding value generation unit 225 selects a rounding value according to the select signal. At step 280, the rounding value generation unit 225 modifies the rounding value. The rounding value may be modified based on the fraction value and/or the rounding mode. Steps 130 through 160 are completed as previously described.

An advantage of using a portion of the input value to perform the rounding operation is that the results for a given input value are deterministic. Specifically, the same output value will be produced for a particular input value regardless of when the rounding operation is performed. In contrast, when a random value is used to perform the rounding operation, the results are not necessarily deterministic. Compared with generating a random value, using a portion of the input value also requires less circuitry. Therefore, the benefit of stochastic rounding (reduced error for successive accumulations) may be achieved without requiring generation of a random value.

Parallel Processing Architecture

FIG. 3 illustrates a parallel processing unit (PPU) 300, in accordance with an embodiment. In an embodiment, the PPU 300 is a multi-threaded processor that is implemented on one or more integrated circuit devices. The PPU 300 is a latency hiding architecture designed to process many threads in parallel. A thread (i.e., a thread of execution) is an instantiation of a set of instructions configured to be executed by the PPU 300. In an embodiment, the PPU 300 is a graphics processing unit (GPU) configured to implement a graphics rendering pipeline for processing three-dimensional (3D) graphics data in order to generate two-dimensional (2D) image data for display on a display device such as a liquid crystal display (LCD) device. In other embodiments, the PPU 300 may be utilized for performing general-purpose computations. While one exemplary parallel processor is provided herein for illustrative purposes, it should be strongly noted that such processor is set forth for illustrative purposes only, and that any processor may be employed to supplement and/or substitute for the same.

One or more PPUs 300 may be configured to accelerate thousands of High Performance Computing (HPC), data center, and machine learning applications. The PPU 300 may be configured to accelerate numerous deep learning systems and applications including autonomous vehicle platforms, deep learning, high-accuracy speech, image, and text recognition systems, intelligent video analytics, molecular simulations, drug discovery, disease diagnosis, weather forecasting, big data analytics, astronomy, molecular dynamics simulation, financial modeling, robotics, factory automation, real-time language translation, online search optimizations, and personalized user recommendations, and the like.

As shown in FIG. 3, the PPU 300 includes an Input/Output (I/O) unit 305, a front end unit 315, a scheduler unit 320, a work distribution unit 325, a hub 330, a crossbar (Xbar) 370, one or more general processing clusters (GPCs) 350, and one or more partition units 380. The PPU 300 may be connected to a host processor or other PPUs 300 via one or more high-speed NVLink 310 interconnect. The PPU 300 may be connected to a host processor or other peripheral devices via an interconnect 302. The PPU 300 may also be connected to a local memory comprising a number of memory devices 304. In an embodiment, the local memory may comprise a number of dynamic random access memory (DRAM) devices. The DRAM devices may be configured as a high-bandwidth memory (HBM) subsystem, with multiple DRAM dies stacked within each device.

The NVLink 310 interconnect enables systems to scale and include one or more PPUs 300 combined with one or more CPUs, supports cache coherence between the PPUs 300 and CPUs, and CPU mastering. Data and/or commands may be transmitted by the NVLink 310 through the hub 330 to/from other units of the PPU 300 such as one or more copy engines, a video encoder, a video decoder, a power management unit, etc. (not explicitly shown). The NVLink 310 is described in more detail in conjunction with FIG. 5B.

The I/O unit 305 is configured to transmit and receive communications (i.e., commands, data, etc.) from a host processor (not shown) over the interconnect 302. The I/O unit 305 may communicate with the host processor directly via the interconnect 302 or through one or more intermediate devices such as a memory bridge. In an embodiment, the I/O unit 305 may communicate with one or more other processors, such as one or more of the PPUs 300 via the interconnect 302. In an embodiment, the I/O unit 305 implements a Peripheral Component Interconnect Express (PCIe) interface for communications over a PCIe bus and the interconnect 302 is a PCIe bus. In alternative embodiments, the I/O unit 305 may implement other types of well-known interfaces for communicating with external devices.

The I/O unit 305 decodes packets received via the interconnect 302. In an embodiment, the packets represent commands configured to cause the PPU 300 to perform various operations. The I/O unit 305 transmits the decoded commands to various other units of the PPU 300 as the commands may specify. For example, some commands may be transmitted to the front end unit 315. Other commands may be transmitted to the hub 330 or other units of the PPU 300 such as one or more copy engines, a video encoder, a video decoder, a power management unit, etc. (not explicitly shown). In other words, the I/O unit 305 is configured to route communications between and among the various logical units of the PPU 300.

In an embodiment, a program executed by the host processor encodes a command stream in a buffer that provides workloads to the PPU 300 for processing. A workload may comprise several instructions and data to be processed by those instructions. The buffer is a region in a memory that is accessible (i.e., read/write) by both the host processor and the PPU 300. For example, the the I/O unit 305 may be configured to access the buffer in a system memory connected to the interconnect 302 via memory requests transmitted over the interconnect 302. In an embodiment, the host processor writes the command stream to the buffer and then transmits a pointer to the start of the command stream to the PPU 300. The front end unit 315 receives pointers to one or more command streams. The front end unit 315 manages the one or more streams, reading commands from the streams and forwarding commands to the various units of the PPU 300.

The front end unit 315 is coupled to a scheduler unit 320 that configures the various GPCs 350 to process tasks defined by the one or more streams. The scheduler unit 320 is configured to track state information related to the various tasks managed by the scheduler unit 320. The state may indicate which GPC 350 a task is assigned to, whether the task is active or inactive, a priority level associated with the task, and so forth. The scheduler unit 320 manages the execution of a plurality of tasks on the one or more GPCs 350.

The scheduler unit 320 is coupled to a work distribution unit 325 that is configured to dispatch tasks for execution on the GPCs 350. The work distribution unit 325 may track a number of scheduled tasks received from the scheduler unit 320. In an embodiment, the work distribution unit 325 manages a pending task pool and an active task pool for each of the GPCs 350. The pending task pool may comprise a number of slots (e.g., 32 slots) that contain tasks assigned to be processed by a particular GPC 350. The active task pool may comprise a number of slots (e.g., 4 slots) for tasks that are actively being processed by the GPCs 350. As a GPC 350 finishes the execution of a task, that task is evicted from the active task pool for the GPC 350 and one of the other tasks from the pending task pool is selected and scheduled for execution on the GPC 350. If an active task has been idle on the GPC 350, such as while waiting for a data dependency to be resolved, then the active task may be evicted from the GPC 350 and returned to the pending task pool while another task in the pending task pool is selected and scheduled for execution on the GPC 350.

The work distribution unit 325 communicates with the one or more GPCs 350 via XBar 370. The XBar 370 is an interconnect network that couples many of the units of the PPU 300 to other units of the PPU 300. For example, the XBar 370 may be configured to couple the work distribution unit 325 to a particular GPC 350. Although not shown explicitly, one or more other units of the PPU 300 may also be connected to the XBar 370 via the hub 330.

The tasks are managed by the scheduler unit 320 and dispatched to a GPC 350 by the work distribution unit 325. The GPC 350 is configured to process the task and generate results. The results may be consumed by other tasks within the GPC 350, routed to a different GPC 350 via the XBar 370, or stored in the memory 304. The results can be written to the memory 304 via the partition units 380, which implement a memory interface for reading and writing data to/from the memory 304. The results can be transmitted to another PPU 304 or CPU via the NVLink 310. In an embodiment, the PPU 300 includes a number U of partition units 380 that is equal to the number of separate and distinct memory devices 304 coupled to the PPU 300. A partition unit 380 will be described in more detail below in conjunction with FIG. 4B.

In an embodiment, a host processor executes a driver kernel that implements an application programming interface (API) that enables one or more applications executing on the host processor to schedule operations for execution on the PPU 300. In an embodiment, multiple compute applications are simultaneously executed by the PPU 300 and the PPU 300 provides isolation, quality of service (QoS), and independent address spaces for the multiple compute applications. An application may generate instructions (i.e., API calls) that cause the driver kernel to generate one or more tasks for execution by the PPU 300. The driver kernel outputs tasks to one or more streams being processed by the PPU 300. Each task may comprise one or more groups of related threads, referred to herein as a warp. In an embodiment, a warp comprises 32 related threads that may be executed in parallel. Cooperating threads may refer to a plurality of threads including instructions to perform the task and that may exchange data through shared memory. Threads and cooperating threads are described in more detail in conjunction with FIG. 5A.

FIG. 4A illustrates a GPC 350 of the PPU 300 of FIG. 3, in accordance with an embodiment. As shown in FIG. 4A, each GPC 350 includes a number of hardware units for processing tasks. In an embodiment, each GPC 350 includes a pipeline manager 410, a pre-raster operations unit (PROP) 415, a raster engine 425, a work distribution crossbar (WDX) 480, a memory management unit (MMU) 490, and one or more Data Processing Clusters (DPCs) 420. It will be appreciated that the GPC 350 of FIG. 4A may include other hardware units in lieu of or in addition to the units shown in FIG. 4A.

In an embodiment, the operation of the GPC 350 is controlled by the pipeline manager 410. The pipeline manager 410 manages the configuration of the one or more DPCs 420 for processing tasks allocated to the GPC 350. In an embodiment, the pipeline manager 410 may configure at least one of the one or more DPCs 420 to implement at least a portion of a graphics rendering pipeline. For example, a DPC 420 may be configured to execute a vertex shader program on the programmable streaming multiprocessor (SM) 440. The pipeline manager 410 may also be configured to route packets received from the work distribution unit 325 to the appropriate logical units within the GPC 350. For example, some packets may be routed to fixed function hardware units in the PROP 415 and/or raster engine 425 while other packets may be routed to the DPCs 420 for processing by the primitive engine 435 or the SM 440. In an embodiment, the pipeline manager 410 may configure at least one of the one or more DPCs 420 to implement a neural network model and/or a computing pipeline.

The PROP unit 415 is configured to route data generated by the raster engine 425 and the DPCs 420 to a Raster Operations (ROP) unit, described in more detail in conjunction with FIG. 4B. The PROP unit 415 may also be configured to perform optimizations for color blending, organize pixel data, perform address translations, and the like.

The raster engine 425 includes a number of fixed function hardware units configured to perform various raster operations. In an embodiment, the raster engine 425 includes a setup engine, a coarse raster engine, a culling engine, a clipping engine, a fine raster engine, and a tile coalescing engine. The setup engine receives transformed vertices and generates plane equations associated with the geometric primitive defined by the vertices. The plane equations are transmitted to the coarse raster engine to generate coverage information (e.g., an x,y coverage mask for a tile) for the primitive. The output of the coarse raster engine is transmitted to the culling engine where fragments associated with the primitive that fail a z-test are culled, and non-culled fragments are transmitted to a clipping engine where fragments lying outside a viewing frustum are clipped. Those fragments that survive clipping and culling may be passed to the fine raster engine to generate attributes for the pixel fragments based on the plane equations generated by the setup engine. The output of the raster engine 425 comprises fragments to be processed, for example, by a fragment shader implemented within a DPC 420.

Each DPC 420 included in the GPC 350 includes an M-Pipe Controller (MPC) 430, a primitive engine 435, and one or more SMs 440. The MPC 430 controls the operation of the DPC 420, routing packets received from the pipeline manager 410 to the appropriate units in the DPC 420. For example, packets associated with a vertex may be routed to the primitive engine 435, which is configured to fetch vertex attributes associated with the vertex from the memory 304. In contrast, packets associated with a shader program may be transmitted to the SM 440.

The SM 440 comprises a programmable streaming processor that is configured to process tasks represented by a number of threads. Each SM 440 is multi-threaded and configured to execute a plurality of threads (e.g., 32 threads) from a particular group of threads concurrently. In an embodiment, the SM 440 implements a SIMD (Single-Instruction, Multiple-Data) architecture where each thread in a group of threads (i.e., a warp) is configured to process a different set of data based on the same set of instructions. All threads in the group of threads execute the same instructions. In another embodiment, the SM 440 implements a SIMT (Single-Instruction, Multiple Thread) architecture where each thread in a group of threads is configured to process a different set of data based on the same set of instructions, but where individual threads in the group of threads are allowed to diverge during execution. In an embodiment, a program counter, call stack, and execution state is maintained for each warp, enabling concurrency between warps and serial execution within warps when threads within the warp diverge. In another embodiment, a program counter, call stack, and execution state is maintained for each individual thread, enabling equal concurrency between all threads, within and between warps. When execution state is maintained for each individual thread, threads executing the same instructions may be converged and executed in parallel for maximum efficiency. The SM 440 will be described in more detail below in conjunction with FIG. 5A.

The MMU 490 provides an interface between the GPC 350 and the partition unit 380. The MMU 490 may provide translation of virtual addresses into physical addresses, memory protection, and arbitration of memory requests. In an embodiment, the MMU 490 provides one or more translation lookaside buffers (TLBs) for performing translation of virtual addresses into physical addresses in the memory 304.

FIG. 4B illustrates a memory partition unit 380 of the PPU 300 of FIG. 3, in accordance with an embodiment. As shown in FIG. 4B, the memory partition unit 380 includes a Raster Operations (ROP) unit 450, a level two (L2) cache 460, and a memory interface 470. The memory interface 470 is coupled to the memory 304. Memory interface 470 may implement 32, 64, 128, 1024-bit data buses, or the like, for high-speed data transfer. In an embodiment, the PPU 300 incorporates U memory interfaces 470, one memory interface 470 per pair of partition units 380, where each pair of partition units 380 is connected to a corresponding memory device 304. For example, PPU 300 may be connected to up to Y memory devices 304, such as high bandwidth memory stacks or graphics double-data-rate, version 5, synchronous dynamic random access memory, or other types of persistent storage.

In an embodiment, the memory interface 470 implements an HBM2 memory interface and Y equals half U. In an embodiment, the HBM2 memory stacks are located on the same physical package as the PPU 300, providing substantial power and area savings compared with conventional GDDR5 SDRAM systems. In an embodiment, each HBM2 stack includes four memory dies and Y equals 4, with HBM2 stack including two 128-bit channels per die for a total of 8 channels and a data bus width of 1024 bits.

In an embodiment, the memory 304 supports Single-Error Correcting Double-Error Detecting (SECDED) Error Correction Code (ECC) to protect data. ECC provides higher reliability for compute applications that are sensitive to data corruption. Reliability is especially important in large-scale cluster computing environments where PPUs 300 process very large datasets and/or run applications for extended periods.

In an embodiment, the PPU 300 implements a multi-level memory hierarchy. In an embodiment, the memory partition unit 380 supports a unified memory to provide a single unified virtual address space for CPU and PPU 300 memory, enabling data sharing between virtual memory systems. In an embodiment the frequency of accesses by a PPU 300 to memory located on other processors is traced to ensure that memory pages are moved to the physical memory of the PPU 300 that is accessing the pages more frequently. In an embodiment, the NVLink 310 supports address translation services allowing the PPU 300 to directly access a CPU's page tables and providing full access to CPU memory by the PPU 300.

In an embodiment, copy engines transfer data between multiple PPUs 300 or between PPUs 300 and CPUs. The copy engines can generate page faults for addresses that are not mapped into the page tables. The memory partition unit 380 can then service the page faults, mapping the addresses into the page table, after which the copy engine can perform the transfer. In a conventional system, memory is pinned (i.e., non-pageable) for multiple copy engine operations between multiple processors, substantially reducing the available memory. With hardware page faulting, addresses can be passed to the copy engines without worrying if the memory pages are resident, and the copy process is transparent.

Data from the memory 304 or other system memory may be fetched by the memory partition unit 380 and stored in the L2 cache 460, which is located on-chip and is shared between the various GPCs 350. As shown, each memory partition unit 380 includes a portion of the L2 cache 460 associated with a corresponding memory device 304. Lower level caches may then be implemented in various units within the GPCs 350. For example, each of the SMs 440 may implement a level one (L1) cache. The L1 cache is private memory that is dedicated to a particular SM 440. Data from the L2 cache 460 may be fetched and stored in each of the L1 caches for processing in the functional units of the SMs 440. The L2 cache 460 is coupled to the memory interface 470 and the XBar 370.

The ROP unit 450 performs graphics raster operations related to pixel color, such as color compression, pixel blending, and the like. The ROP unit 450 also implements depth testing in conjunction with the raster engine 425, receiving a depth for a sample location associated with a pixel fragment from the culling engine of the raster engine 425. The depth is tested against a corresponding depth in a depth buffer for a sample location associated with the fragment. If the fragment passes the depth test for the sample location, then the ROP unit 450 updates the depth buffer and transmits a result of the depth test to the raster engine 425. It will be appreciated that the number of partition units 380 may be different than the number of GPCs 350 and, therefore, each ROP unit 450 may be coupled to each of the GPCs 350. The ROP unit 450 tracks packets received from the different GPCs 350 and determines which GPC 350 that a result generated by the ROP unit 450 is routed to through the Xbar 370. Although the ROP unit 450 is included within the memory partition unit 380 in FIG. 4B, in other embodiment, the ROP unit 450 may be outside of the memory partition unit 380. For example, the ROP unit 450 may reside in the GPC 350 or another unit.

FIG. 5A illustrates the streaming multi-processor 440 of FIG. 4A, in accordance with an embodiment. As shown in FIG. 5A, the SM 440 includes an instruction cache 505, one or more scheduler units 510, a register file 520, one or more processing cores 550, one or more special function units (SFUs) 552, one or more load/store units (LSUs) 554, an interconnect network 580, a shared memory/L1 cache 570.

As described above, the work distribution unit 325 dispatches tasks for execution on the GPCs 350 of the PPU 300. The tasks are allocated to a particular DPC 420 within a GPC 350 and, if the task is associated with a shader program, the task may be allocated to an SM 440. The scheduler unit 510 receives the tasks from the work distribution unit 325 and manages instruction scheduling for one or more thread blocks assigned to the SM 440. The scheduler unit 510 schedules thread blocks for execution as warps of parallel threads, where each thread block is allocated at least one warp. In an embodiment, each warp executes 32 threads. The scheduler unit 510 may manage a plurality of different thread blocks, allocating the warps to the different thread blocks and then dispatching instructions from the plurality of different cooperative groups to the various functional units (i.e., cores 550, SFUs 552, and LSUs 554) during each clock cycle.

Cooperative Groups is a programming model for organizing groups of communicating threads that allows developers to express the granularity at which threads are communicating, enabling the expression of richer, more efficient parallel decompositions. Cooperative launch APIs support synchronization amongst thread blocks for the execution of parallel algorithms. Conventional programming models provide a single, simple construct for synchronizing cooperating threads: a barrier across all threads of a thread block (i.e., the syncthreads( ) function). However, programmers would often like to define groups of threads at smaller than thread block granularities and synchronize within the defined groups to enable greater performance, design flexibility, and software reuse in the form of collective group-wide function interfaces.

Cooperative Groups enables programmers to define groups of threads explicitly at sub-block (i.e., as small as a single thread) and multi-block granularities, and to perform collective operations such as synchronization on the threads in a cooperative group. The programming model supports clean composition across software boundaries, so that libraries and utility functions can synchronize safely within their local context without having to make assumptions about convergence. Cooperative Groups primitives enable new patterns of cooperative parallelism, including producer-consumer parallelism, opportunistic parallelism, and global synchronization across an entire grid of thread blocks.

A dispatch unit 515 is configured to transmit instructions to one or more of the functional units. In the embodiment, the scheduler unit 510 includes two dispatch units 515 that enable two different instructions from the same warp to be dispatched during each clock cycle. In alternative embodiments, each scheduler unit 510 may include a single dispatch unit 515 or additional dispatch units 515.

Each SM 440 includes a register file 520 that provides a set of registers for the functional units of the SM 440. In an embodiment, the register file 520 is divided between each of the functional units such that each functional unit is allocated a dedicated portion of the register file 520. In another embodiment, the register file 520 is divided between the different warps being executed by the SM 440. The register file 520 provides temporary storage for operands connected to the data paths of the functional units.

Each SM 440 comprises L processing cores 550. In an embodiment, the SM 440 includes a large number (e.g., 128, etc.) of distinct processing cores 550. Each core 550 may include a fully-pipelined, single-precision, double-precision, and/or mixed precision processing unit that includes a floating-point arithmetic logic unit and an integer arithmetic logic unit. In an embodiment, the floating-point arithmetic logic units implement the IEEE 754-2008 standard for floating-point arithmetic. In an embodiment, the cores 550 include 64 single-precision (32-bit) floating-point cores, 64 integer cores, 32 double-precision (64-bit) floating-point cores, and 8 tensor cores. In an embodiment, the cores 550 are configured to perform rounding operations using the method 100 or 260.

Tensor cores are configured to perform matrix operations, and, in an embodiment, one or more tensor cores are included in the cores 550. In particular, the tensor cores are configured to perform deep learning matrix arithmetic, such as convolution operations for neural network training and inferencing. In an embodiment, each tensor core operates on a 4×4 matrix and performs a matrix multiply and accumulate operation D=A×B+C, where A, B, C, and D are 4×4 matrices. In an embodiment, the tensor cores are configured to perform rounding operations using the method 100 or 260.

In an embodiment, the matrix multiply inputs A and B are 16-bit floating-point matrices, while the accumulation matrices C and D may be 16-bit floating-point or 32-bit floating-point matrices. Tensor Cores operate on 16-bit floating-point input data with 32-bit floating-point accumulation. The 16-bit floating-point multiply requires 64 operations and results in a full precision product that is then accumulated using 32-bit floating-point addition with the other intermediate products for a 4×4×4 matrix multiply. In practice, Tensor Cores are used to perform much larger two-dimensional or higher dimensional matrix operations, built up from these smaller elements. An API, such as CUDA 9 C++ API, exposes specialized matrix load, matrix multiply and accumulate, and matrix store operations to efficiently use Tensor Cores from a CUDA-C++ program. At the CUDA level, the warp-level interface assumes 16×16 size matrices spanning all 32 threads of the warp.

Each SM 440 also comprises M SFUs 552 that perform special functions (e.g., attribute evaluation, reciprocal square root, and the like). In an embodiment, the SFUs 552 are configured to perform rounding operations using the method 100 or 260. In an embodiment, the SFUs 552 may include a tree traversal unit configured to traverse a hierarchical tree data structure. In an embodiment, the SFUs 552 may include texture unit configured to perform texture map filtering operations. In an embodiment, the texture units are configured to load texture maps (e.g., a 2D array of texels) from the memory 304 and sample the texture maps to produce sampled texture values for use in shader programs executed by the SM 440. In an embodiment, the texture maps are stored in the shared memory/L1 cache 470. The texture units implement texture operations such as filtering operations using mip-maps (i.e., texture maps of varying levels of detail). In an embodiment, each SM 340 includes two texture units.

Each SM 440 also comprises N LSUs 554 that implement load and store operations between the shared memory/L1 cache 570 and the register file 520. Each SM 440 includes an interconnect network 580 that connects each of the functional units to the register file 520 and the LSU 554 to the register file 520, shared memory/L1 cache 570. In an embodiment, the interconnect network 580 is a crossbar that can be configured to connect any of the functional units to any of the registers in the register file 520 and connect the LSUs 554 to the register file and memory locations in shared memory/L1 cache 570.

The shared memory/L1 cache 570 is an array of on-chip memory that allows for data storage and communication between the SM 440 and the primitive engine 435 and between threads in the SM 440. In an embodiment, the shared memory/L1 cache 570 comprises 128 KB of storage capacity and is in the path from the SM 440 to the partition unit 380. The shared memory/L1 cache 570 can be used to cache reads and writes. One or more of the shared memory/L1 cache 570, L2 cache 460, and memory 304 are backing stores.

Combining data cache and shared memory functionality into a single memory block provides the best overall performance for both types of memory accesses. The capacity is usable as a cache by programs that do not use shared memory. For example, if shared memory is configured to use half of the capacity, texture and load/store operations can use the remaining capacity. Integration within the shared memory/L1 cache 570 enables the shared memory/L1 cache 570 to function as a high-throughput conduit for streaming data while simultaneously providing high-bandwidth and low-latency access to frequently reused data.

When configured for general purpose parallel computation, a simpler configuration can be used compared with graphics processing. Specifically, the fixed function graphics processing units shown in FIG. 3, are bypassed, creating a much simpler programming model. In the general purpose parallel computation configuration, the work distribution unit 325 assigns and distributes blocks of threads directly to the DPCs 420. The threads in a block execute the same program, using a unique thread ID in the calculation to ensure each thread generates unique results, using the SM 440 to execute the program and perform calculations, shared memory/L1 cache 570 to communicate between threads, and the LSU 554 to read and write global memory through the shared memory/L1 cache 570 and the memory partition unit 380. When configured for general purpose parallel computation, the SM 440 can also write commands that the scheduler unit 320 can use to launch new work on the DPCs 420.

The PPU 300 may be included in a desktop computer, a laptop computer, a tablet computer, servers, supercomputers, a smart-phone (e.g., a wireless, hand-held device), personal digital assistant (PDA), a digital camera, a vehicle, a head mounted display, a hand-held electronic device, and the like. In an embodiment, the PPU 300 is embodied on a single semiconductor substrate. In another embodiment, the PPU 300 is included in a system-on-a-chip (SoC) along with one or more other devices such as additional PPUs 300, the memory 204, a reduced instruction set computer (RISC) CPU, a memory management unit (MMU), a digital-to-analog converter (DAC), and the like.

In an embodiment, the PPU 300 may be included on a graphics card that includes one or more memory devices 304. The graphics card may be configured to interface with a PCIe slot on a motherboard of a desktop computer. In yet another embodiment, the PPU 300 may be an integrated graphics processing unit (iGPU) or parallel processor included in the chipset of the motherboard.

Exemplary Computing System

Systems with multiple GPUs and CPUs are used in a variety of industries as developers expose and leverage more parallelism in applications such as artificial intelligence computing. High-performance GPU-accelerated systems with tens to many thousands of compute nodes are deployed in data centers, research facilities, and supercomputers to solve ever larger problems. As the number of processing devices within the high-performance systems increases, the communication and data transfer mechanisms need to scale to support the increased bandwidth.

FIG. 5B is a conceptual diagram of a processing system 500 implemented using the PPU 300 of FIG. 3, in accordance with an embodiment. The exemplary system 565 may be configured to implement the method 100 shown in FIG. 1. The processing system 500 includes a CPU 530, switch 510, and multiple PPUs 300 each and respective memories 304. The NVLink 310 provides high-speed communication links between each of the PPUs 300. Although a particular number of NVLink 310 and interconnect 302 connections are illustrated in FIG. 5B, the number of connections to each PPU 300 and the CPU 530 may vary. The switch 510 interfaces between the interconnect 302 and the CPU 530. The PPUs 300, memories 304, and NVLinks 310 may be situated on a single semiconductor platform to form a parallel processing module 525. In an embodiment, the switch 510 supports two or more protocols to interface between various different connections and/or links.

In another embodiment (not shown), the NVLink 310 provides one or more high-speed communication links between each of the PPUs 300 and the CPU 530 and the switch 510 interfaces between the interconnect 302 and each of the PPUs 300. The PPUs 300, memories 304, and interconnect 302 may be situated on a single semiconductor platform to form a parallel processing module 525. In yet another embodiment (not shown), the interconnect 302 provides one or more communication links between each of the PPUs 300 and the CPU 530 and the switch 510 interfaces between each of the PPUs 300 using the NVLink 310 to provide one or more high-speed communication links between the PPUs 300. In another embodiment (not shown), the NVLink 310 provides one or more high-speed communication links between the PPUs 300 and the CPU 530 through the switch 510. In yet another embodiment (not shown), the interconnect 302 provides one or more communication links between each of the PPUs 300 directly. One or more of the NVLink 310 high-speed communication links may be implemented as a physical NVLink interconnect or either an on-chip or on-die interconnect using the same protocol as the NVLink 310.

In the context of the present description, a single semiconductor platform may refer to a sole unitary semiconductor-based integrated circuit fabricated on a die or chip. It should be noted that the term single semiconductor platform may also refer to multi-chip modules with increased connectivity which simulate on-chip operation and make substantial improvements over utilizing a conventional bus implementation. Of course, the various circuits or devices may also be situated separately or in various combinations of semiconductor platforms per the desires of the user. Alternately, the parallel processing module 525 may be implemented as a circuit board substrate and each of the PPUs 300 and/or memories 304 may be packaged devices. In an embodiment, the CPU 530, switch 510, and the parallel processing module 525 are situated on a single semiconductor platform.

In an embodiment, the signaling rate of each NVLink 310 is 20 to 25 Gigabits/second and each PPU 300 includes six NVLink 310 interfaces (as shown in FIG. 5B, five NVLink 310 interfaces are included for each PPU 300). Each NVLink 310 provides a data transfer rate of 25 Gigabytes/second in each direction, with six links providing 300 Gigabytes/second. The NVLinks 310 can be used exclusively for PPU-to-PPU communication as shown in FIG. 5B, or some combination of PPU-to-PPU and PPU-to-CPU, when the CPU 530 also includes one or more NVLink 310 interfaces.

In an embodiment, the NVLink 310 allows direct load/store/atomic access from the CPU 530 to each PPU's 300 memory 304. In an embodiment, the NVLink 310 supports coherency operations, allowing data read from the memories 304 to be stored in the cache hierarchy of the CPU 530, reducing cache access latency for the CPU 530. In an embodiment, the NVLink 310 includes support for Address Translation Services (ATS), allowing the PPU 300 to directly access page tables within the CPU 530. One or more of the NVLinks 310 may also be configured to operate in a low-power mode.

FIG. 5C illustrates an exemplary system 565 in which the various architecture and/or functionality of the various previous embodiments may be implemented. The exemplary system 565 may be configured to implement the method 100 shown in FIG. 1 or the method 260 shown in FIG. 2D.

As shown, a system 565 is provided including at least one central processing unit 530 that is connected to a communication bus 575. The communication bus 575 may be implemented using any suitable protocol, such as PCI (Peripheral Component Interconnect), PCI-Express, AGP (Accelerated Graphics Port), HyperTransport, or any other bus or point-to-point communication protocol(s). The system 565 also includes a main memory 540. Control logic (software) and data are stored in the main memory 540 which may take the form of random access memory (RAM).

The system 565 also includes input devices 560, the parallel processing system 525, and display devices 545, i.e. a conventional CRT (cathode ray tube), LCD (liquid crystal display), LED (light emitting diode), plasma display or the like. User input may be received from the input devices 560, e.g., keyboard, mouse, touchpad, microphone, and the like. Each of the foregoing modules and/or devices may even be situated on a single semiconductor platform to form the system 565. Alternately, the various modules may also be situated separately or in various combinations of semiconductor platforms per the desires of the user.

Further, the system 565 may be coupled to a network (e.g., a telecommunications network, local area network (LAN), wireless network, wide area network (WAN) such as the Internet, peer-to-peer network, cable network, or the like) through a network interface 535 for communication purposes.

The system 565 may also include a secondary storage (not shown). The secondary storage 610 includes, for example, a hard disk drive and/or a removable storage drive, representing a floppy disk drive, a magnetic tape drive, a compact disk drive, digital versatile disk (DVD) drive, recording device, universal serial bus (USB) flash memory. The removable storage drive reads from and/or writes to a removable storage unit in a well-known manner.

Computer programs, or computer control logic algorithms, may be stored in the main memory 540 and/or the secondary storage. Such computer programs, when executed, enable the system 565 to perform various functions. The memory 540, the storage, and/or any other storage are possible examples of computer-readable media.

The architecture and/or functionality of the various previous figures may be implemented in the context of a general computer system, a circuit board system, a game console system dedicated for entertainment purposes, an application-specific system, and/or any other desired system. For example, the system 565 may take the form of a desktop computer, a laptop computer, a tablet computer, servers, supercomputers, a smart-phone (e.g., a wireless, hand-held device), personal digital assistant (PDA), a digital camera, a vehicle, a head mounted display, a hand-held electronic device, a mobile phone device, a television, workstation, game consoles, embedded system, and/or any other type of logic.

Machine Learning

Deep neural networks (DNNs) developed on processors, such as the PPU 300 have been used for diverse use cases, from self-driving cars to faster drug development, from automatic image captioning in online image databases to smart real-time language translation in video chat applications. Deep learning is a technique that models the neural learning process of the human brain, continually learning, continually getting smarter, and delivering more accurate results more quickly over time. A child is initially taught by an adult to correctly identify and classify various shapes, eventually being able to identify shapes without any coaching. Similarly, a deep learning or neural learning system needs to be trained in object recognition and classification for it get smarter and more efficient at identifying basic objects, occluded objects, etc., while also assigning context to objects.

At the simplest level, neurons in the human brain look at various inputs that are received, importance levels are assigned to each of these inputs, and output is passed on to other neurons to act upon. An artificial neuron or perceptron is the most basic model of a neural network. In one example, a perceptron may receive one or more inputs that represent various features of an object that the perceptron is being trained to recognize and classify, and each of these features is assigned a certain weight based on the importance of that feature in defining the shape of an object.

A deep neural network (DNN) model includes multiple layers of many connected perceptrons (e.g., nodes) that can be trained with enormous amounts of input data to quickly solve complex problems with high accuracy. In one example, a first layer of the DLL model breaks down an input image of an automobile into various sections and looks for basic patterns such as lines and angles. The second layer assembles the lines to look for higher level patterns such as wheels, windshields, and mirrors. The next layer identifies the type of vehicle, and the final few layers generate a label for the input image, identifying the model of a specific automobile brand.

Once the DNN is trained, the DNN can be deployed and used to identify and classify objects or patterns in a process known as inference. Examples of inference (the process through which a DNN extracts useful information from a given input) include identifying handwritten numbers on checks deposited into ATM machines, identifying images of friends in photos, delivering movie recommendations to over fifty million users, identifying and classifying different types of automobiles, pedestrians, and road hazards in driverless cars, or translating human speech in real-time.

During training, data flows through the DNN in a forward propagation phase until a prediction is produced that indicates a label corresponding to the input. If the neural network does not correctly label the input, then errors between the correct label and the predicted label are analyzed, and the weights are adjusted for each feature during a backward propagation phase until the DNN correctly labels the input and other inputs in a training dataset. Training complex neural networks requires massive amounts of parallel computing performance, including floating-point multiplications and additions that are supported by the PPU 300. Inferencing is less compute-intensive than training, being a latency-sensitive process where a trained neural network is applied to new inputs it has not seen before to classify images, translate speech, and generally infer new information.

Neural networks rely heavily on matrix math operations, and complex multi-layered networks require tremendous amounts of floating-point performance and bandwidth for both efficiency and speed. With thousands of processing cores, optimized for matrix math operations, and delivering tens to hundreds of TFLOPS of performance, the PPU 300 is a computing platform capable of delivering performance required for deep neural network-based artificial intelligence and machine learning applications.

While various embodiments have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of a preferred embodiment should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents. 

What is claimed is:
 1. A circuit for rounding an input value to produce a rounded output value, configured to: receive an input value, wherein the input value comprises a first set of bits; identify a rounding value from the input value, wherein the rounding value is a second set of bits, and wherein the second set of bits comprises a first portion of the first set of bits; extract a second value from the input value, wherein the second value is a third set of bits, wherein the third set of bits comprises a second portion of the first set of bits; add the second value and the rounding value to produce a sum; and truncate the sum to produce a rounded output value.
 2. The circuit of claim 1, wherein the input value is represented in a floating-point format having a mantissa and an exponent.
 3. The circuit of claim 2, wherein the rounding value is a portion of the mantissa.
 4. The circuit of claim 1, wherein the input value is represented in a fixed-point format.
 5. The circuit of claim 1, wherein the second set of bits, which is the rounding value, are the least significant bits of the input value, which is represented in a fixed-point format.
 6. The circuit of claim 1, wherein the rounded output value is an integer.
 7. The circuit of claim 1, wherein number of bits to be truncated from the sum is fixed, computed, or programmable.
 8. The circuit of claim 1, further configured to: align the rounding value and the second value at a rounding position.
 9. The circuit of claim 1, wherein the third set of bits is all or some of the first set of bits of the input value.
 10. The circuit of claim 1, wherein the circuit is deterministic in that each time the circuit receives a particular input value, the circuit produces a same corresponding rounded output value each time.
 11. A method for rounding an input value to produce a rounded output value, comprising: receiving an input value, wherein the input value comprises a first set of bits; identifying a rounding value from the input value, wherein the rounding value is a second set of bits, and wherein the second set of bits comprises a first portion of the first set of bits; extracting a second value from the input value, wherein the second value is a third set of bits, wherein the third set of bits comprises a second portion of the first set of bits; adding the second value and the rounding value to produce a sum; and truncating the sum to produce a rounded output value.
 12. The method of claim 11, wherein the input value is represented in a floating-point format having a mantissa and an exponent.
 13. The method of claim 12, wherein the rounding value is a portion of the mantissa.
 14. The method of claim 11, wherein the input value is represented in a fixed-point format.
 15. The method of claim 11, wherein the second set of bits, which is the rounding value, are the least significant bits of the input value, which is represented in a fixed-point format.
 16. The method of claim 11, wherein the rounded output value is an integer.
 17. The method of claim 11, wherein number of bits to be truncated from the sum is fixed, computed, or programmable.
 18. The method of claim 11, further comprising: aligning the rounding value and the second value at a rounding position.
 19. The method of claim 11, wherein the third set of bits is all or some of the first set of bits of the input value.
 20. The method of claim 11, wherein the method is deterministic in that each time the method receives a particular input value, the method produces a same corresponding rounded output value each time. 